Newton, Isaac, Philosophia naturalis principia mathematica, 1713
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                  DE MOTU
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                  CORPORUM</s>
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                  <s>
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                  Scholium.
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                  <s>Eadem ratione qua prodiit denſitas Medii ut (SX
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                  AC
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                  /RX
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                  HT
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                  ) in Co­
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                  rollario primo, ſi reſiſtentia ponatur ut velocitatis V dignitas quæ­
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                  libet V
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
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                    <emph.end type="sup"/>
                  prodibit denſitas Medii ut (S/R(4-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  /2))X(—
                    <emph type="italics"/>
                  AC/HT
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                  |
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
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                  -1.
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                  ) </s>
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                <p type="main">
                  <s>Et propterea ſi Curva inveniri poteſt ea lege ut data fuerit ratio
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                  (S/R(4-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  /2)) ad (—
                    <emph type="italics"/>
                  HT/AC
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                  |
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
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                  -1
                    <emph.end type="sup"/>
                  ), vel (S
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  /R
                    <emph type="sup"/>
                  4-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ) ad (—1+QQ|
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  ): corpus move­
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                  bitur in hac Curva in uniformi Medio cum reſiſtentia quæ ſit ut
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                  velocitatis dignitas V
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
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                    <emph.end type="sup"/>
                  . </s>
                  <s>Sed redeamus ad Curvas ſimpliciores. </s>
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                <p type="main">
                  <s>Quoniam motus non fit in Parabola niſi in Medio non reſiſten­
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                  te, in Hyperbolis vero hic deſcriptis fit per reſiſtentiam perpetuam;
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                  perſpicuum eſt quod Linea, quam projectile in Medio uniformiter
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                  reſiſtente deſcribit, propius accedit ad Hyperbolas haſce quam ad
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                  Parabolam. </s>
                  <s>Eſt utique linea illa Hyperbolici generis, ſed quæ
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                  circa verticem magis diſtat ab Aſymptotis; in partibus a vertice
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                  remotioribus propius ad ipſas accedit quam pro ratione Hyper­
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                  bolarum quas hic deſcripſi. </s>
                  <s>Tanta vero non eſt inter has & illam
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                  differentia, quin illius loco poſſint hæ in rebus practicis non in­
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                  commode adhiberi. </s>
                  <s>Et utiliores forſan futuræ ſunt hæ, quam
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                  Hyperbola magis accurata & ſimul magis compoſita. </s>
                  <s>Ipſæ vero
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                  in uſum ſic deducentur. </s>
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                <p type="main">
                  <s>Compleatur parallelogrammum
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                  XYGT,
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                  & recta
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                  GT
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                  tanget
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                  Hyperbolam in
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                  G,
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                  ideoQ.E.D.nſitas Medii in
                    <emph type="italics"/>
                  G
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                  eſt reciproce ut
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                  tangens
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                  GT,
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                  & velocitas ibidem ut √(
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                  GTq/GV
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                  ), reſiſtentia autem ad
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                  vim gravitatis ut
                    <emph type="italics"/>
                  GT
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                  ad
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                  (2nn+2n/n+2)GV.
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                  </s>
                </p>
                <p type="main">
                  <s>Proinde ſi corpus de loco
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                  A
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                  ſecundum rectam
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                  AH
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                  projectum
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                  deſcribat Hyperbolam
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                  AGK,
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                  &
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                  AH
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                  producta occurrat Aſymp­
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                  toto
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                  MX
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                  in
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                  H,
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                  actaque
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                  AI
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                  eidem parallela occurrat alteri Aſymp­
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                  toto
                    <emph type="italics"/>
                  MX
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                  in
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                  I
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                  : erit Medii denſitas in
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                  A
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                  reciproce ut
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                  AH,
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                  & cor­
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                  poris velocitas ut √(
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                  AHq/AI
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                  ), ac reſiſtentia ibidem ad gravitatem ut
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                    <emph type="italics"/>
                  AH
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                  ad (
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                  2nn+2n/n+2
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                  ) in
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                  AI.
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                  Unde prodeunt ſequentes Regulæ. </s>
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